In general, the 6pm news reached its peak for almost 5 million viewers per day in the first month.

This is actually quite communicative and in IELTS this sentence might give you a satisfactory score for TA. However, the language problems would leave you with a much lower score for GRA and for CC.

It doesn’t make sense to signal this statement ‘In general‘, because it’s not general. It features data values taken from the x and y axes of the graph. Better to put this information in the detail section of your essay and signal it “In detail,“.

You need to treat ‘reach a peak‘ as a phrasal verb. If you want to change the tense – and the tense will most likely be past simple tense – then you can modify ‘reach‘ (past: ‘reached a peak‘). Otherwise don’t mess with ‘a‘ and don’t mess with ‘peak‘.

The preposition ‘for‘ is not right.

So, if you really are making a general statement, do this:

In general, the popularity of the 6pm news reached a peak in the first month.

If you want to mention detail, then do this:

In detail, the 6pm news reached a peakof almost 5 million viewers per day in the first month.